Question

Simplify Expressions -

$\frac{\sqrt{810c^3{d}^7}}{\sqrt{1000c^{5}d}}$

Short answer

The simplification of Expression will be - $\frac{9d^3}{10c}$

Step-by-step solution

Step 1.  Given Data

Expressions -

$\frac{\sqrt{810c^3{d}^7}}{\sqrt{1000c^{5}d}}$

Step 2.  To Find 

Simplify The Expressions

Step 3.  Explanation 

Expressions - $\frac{\sqrt{810c^3{d}^7}}{\sqrt{1000c^{5}d}}$

Neither radicand is a perfect square, so rewrite using the quotient property of square roots -

$$\begin{gathered} \frac{\sqrt{810c^3{d}^7}}{\sqrt{1000c^{5}d}} \\ \sqrt{\frac{810c^3{d}^7}{1000c^{5}d}} \end{gathered}$$

Step 4.  Calculation 

Remove common factors in the numerator and denominator.

$$\begin{gathered} \sqrt{\frac{810c^3{d}^7}{1000c^{5}d}} \\ \sqrt{\frac{81\times 10\times c^3\times d^6\times d}{100\times 10\times c^3\times c^2\times d}} \\ \sqrt{\frac{81d^6}{100c^2}} \end{gathered}$$

simplify-

$$\begin{gathered} \sqrt{\frac{81d^6}{100c^2}} \\ \frac{9d^3}{10c} \end{gathered}$$